\(f(R)\)  gravity is an important and well-studied class of modified gravity theories [1]}, [2]}. Many important cosmological models, for example Starobinsky's inflationary models [3]} and Hu-Sawicki's late time cosmology model [4]}, employ these theories to explain the late-time acceleration of the universe, without the need for dark energy. The field equations for \(f(R)\)  gravity are comprised of a modified Friedmann equation, a modified Raychaudhuri equation and the continuity equation for the cosmological fluid. In general they constitute a complicated set of coupled non-linear partial differential equations. In cosmology we mostly work with homogeneous metrics in order to respect the cosmological principle, so that the cosmological field equations reduce to a set of coupled non-linear ordinary differential equations. As we know, there are no generic method to solve non-linear differential equations, so the method of dynamical system can be a good approach to extract qualitative and qualitative information about the evolution of such non-linear systems. In the dynamical system formulation of cosmology, a set of dimensionless expansion normalised dynamical variables are suitably defined in order that the cosmological field equations can be written in as a closed set of coupled first order nonlinear differential equations, constituting a dynamical system [5]}, [6]}. The phase trajectories in the corresponding phase space represent all possible cosmological dynamics within the model under consideration. The fixed points are interpreted as cosmic epochs, with unstable fixed points (repelers or past attractors), saddle fixed points and stable fixed points (attractors or future attractors) representing possible initial, intermediate and final epochs of the cosmic evolution.
